Improved CMB anisotropy constraints on primordial magnetic fields from the post-recombination ionization history

TL;DR

This paper constrains primordial magnetic fields by analyzing their effects on the ionization history and CMB, extending previous work to arbitrary spectral indices and deriving upper bounds on their amplitude.

Contribution

It introduces a method to constrain PMFs with arbitrary spectral indices using their impact on ionization history and CMB, improving previous scale-invariant spectrum analyses.

Findings

Upper bound on PMF amplitude: <0.83 nG.

Ambipolar diffusion dominates for positive spectral index.

MHD turbulence is more relevant for negative spectral index.

Abstract

We investigate the impact of a stochastic background of Primordial Magnetic Fields (PMF) generated before recombination on the ionization history of the Universe and on the Cosmic Microwave Background radiation (CMB). Pre-recombination PMFs are dissipated during recombination and reionization via decaying MHD turbulence and ambipolar diffusion. This modifies the local matter and electron temperatures and thus affects the ionization history and Thomson visibility function. We use this effect to constrain PMFs described by a spectrum of power-law type, extending our previous study (based on a scale-invariant spectrum) to arbitrary spectral index. We derive upper bounds on the integrated amplitude of PMFs due to the separate effect of ambipolar diffusion and MHD decaying turbulence and their combination. We show that ambipolar diffusion is relevant for $n_{\rm B}>0$ whereas for $n_{\rm B}<0$ MHD turbulence is more important. The bound marginalized over the spectral index on the integrated amplitude of PMFs with a sharp cut-off is $\sqrt{\langle B^2 \rangle}<0.83$ nG. We discuss the quantitative relevance of the assumptions on the damping mechanism and the comparison with previous bounds.